"... Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are rec ..."

Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean. The continuous-time financial theory has developed extensive tools to price derivative securities when the underlying traded asset(s) or nontraded factor(s) follow stochastic differential equations [see Merton (1990) for examples]. However, as a practical matter, how to specify an appropriate stochastic differential equation is for the most part an unanswered question. For example, many different continuous-time The comments and suggestions of Kerry Back (the editor) and an anonymous referee were very helpful. I am also grateful to George Constantinides,

"... Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach, which focuses on accurately fitting the cross sectio ..."

Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach, which focuses on accurately fitting the cross section of interest rates at any given time but neglects time-series dynamics, nor the equilibrium approach, which focuses on time-series dynamics (primarily those of the instantaneous rate) but pays comparatively little attention to fitting the entire cross section at any given time and has been shown to forecast poorly. Instead, we use variations on the Nelson-Siegel exponential components framework to model the entire yield curve, period-by-period, as a three-dimensional parameter evolving dynamically. We show that the three time-varying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce term-structure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts. Finally, we discuss a number of extensions, including generalized duration measures, applications to active bond portfolio management, and arbitrage-free specifications. Acknowledgments: The National Science Foundation and the Wharton Financial Institutions Center provided research support. For helpful comments we are grateful to Dave Backus, Rob Bliss, Michael Brandt, Todd Clark, Qiang Dai, Ron Gallant, Mike Gibbons, Da...

"... Moody's Investors Service for financial support and for making their historical data on company ratings available to us. We are grateful to GFI for making their data on CDS spreads available to us. We are also grateful to Jeff Bohn, Richard Cantor, Yu Du, Darrell ..."

Moody&apos;s Investors Service for financial support and for making their historical data on company ratings available to us. We are grateful to GFI for making their data on CDS spreads available to us. We are also grateful to Jeff Bohn, Richard Cantor, Yu Du, Darrell

"... Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of Poisson-Gaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short ra ..."

Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of Poisson-Gaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Estimators are used based on analytical derivations of the characteristic functions and moments of jump-diffusion stochastic processes for a range of jump distributions, and are extended to discrete-time models. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing models would be well-enhanced by jump and ARCH-type processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the non-linearity of interest rate drifts, so prevalent in pure-diffusion models. Day-of-week effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.

"... This paper provides an empirical analysis of the role of jumps in continuous-time models of the short rate. Statistically, if jumps are present di¤usion models are misspeci…ed and I develop a test to detect jump-induced misspeci…cation. After …nding evidence for jumps, I introduce a nonparametric ju ..."

This paper provides an empirical analysis of the role of jumps in continuous-time models of the short rate. Statistically, if jumps are present di¤usion models are misspeci…ed and I develop a test to detect jump-induced misspeci…cation. After …nding evidence for jumps, I introduce a nonparametric jump-di¤usion model and develop an estimation methodology. The results point toward a dominant statistical role for jumps in determining the dynamics of the short rate relative to di¤usive components. Estimates of jump times and sizes indicate that jumps serve an interesting economic purpose: they provide a main conduit for information about the macroeconomy to enter the term structure. Finally, I investigate the pricing implications of jumps. While jumps do not appear to have a large impact on the cross-section of bond prices, they do have important implications for interest rate derivatives.

We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on the canonical representation of affine models greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage. † For helpful comments we thank seminar/conference participants at the University of Chicago, Copenhagen

"... This paper develops an arbitrage-free time-series model of yields in continuous time that incorporates central bank policy. Policy-related events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linear-quadratic jump ..."

This paper develops an arbitrage-free time-series model of yields in continuous time that incorporates central bank policy. Policy-related events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linear-quadratic jump-diffusions as state variables, which allows for a wide variety of jump types but still leads to tractable solutions for bond prices. I estimate a version of this model with U.S. interest rates, the Federal Reserve’s target rate, and key macroeconomic aggregates. The estimated model improves bond pricing, especially at short maturities. The “snake-shape ” of the volatility curve is linked to monetary policy inertia. A new monetary policy shock series is obtained by assuming that the Fed reacts to information available right before the FOMC meeting. According to the estimated policy rule, the Fed is mainly reacting to information contained in the yield-curve. Surprises in analyst forecasts turn out to be merely temporary components of macro variables, so that the “hump-shaped” yield response to these surprises is not consistent with a Taylor-type policy rule.

"... We investigate whether the same finite dimensional dynamic system spans both interest rates (the yield curve) and interest rate options (the implied volatility surface). We find that the options market exhibits factors independent of the underlying yield curve. While three common factors are adeq ..."

We investigate whether the same finite dimensional dynamic system spans both interest rates (the yield curve) and interest rate options (the implied volatility surface). We find that the options market exhibits factors independent of the underlying yield curve. While three common factors are adequate to capture the systematic movement of the yield curve, we need three additional factors to capture the movement of the implied volatility surface. JEL Classification Codes: E43, G12. Key Words: Factors; principal component; LIBOR; swaps; swaptions; yield curve; implied volatility surface. We measure and interpret common factors underlying the US dollar LIBOR market that includes both interest rates and interest rate options. In particular, we investigate whether the same finite dimensional dynamic system spans both types of instruments. We find that the options market exhibits factors independent of the underlying yield curve. We identify three common factors from LIBOR and swap rat...

"... In this paper, we analyze the economic value of predicting index returns as well as volatility. On the basis of fairly simple linear models, estimated recursively, we produce genuine out-of-sample forecasts for the return on the S&P 500 index and its volatility. Using monthly data from 1954 t ..."

In this paper, we analyze the economic value of predicting index returns as well as volatility. On the basis of fairly simple linear models, estimated recursively, we produce genuine out-of-sample forecasts for the return on the S&amp;P 500 index and its volatility. Using monthly data from 1954 to 1998, we test the statistical significance of return and volatility predictability and examine the economic value of a number of alternative trading strategies.